Abstract

The principle of an optical technique for simultaneous velocity, size, and concentration in suspension measurements of spherical droplets and cylindrical jets is proposed. This technique is based on phase Doppler anemometry working in the dual burst technique configuration. The particle size and velocity are deduced from the reflected signal phase and frequency, whereas the amplitude ratio between the refracted and the reflected signals is used for measuring the concentration of small scatterers inside the particles. Numerical simulations, based on geometrical optics and a Monte Carlo model, and an experimental validation test on cylindrical jets made of various suspensions, are used to validate the principle of the proposed technique. It is believed that this new technique could be useful in investigating processes in which liquid suspensions are sprayed for surface coating, drying, or combustion applications.

© 1999 Optical Society of America

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References

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  1. J. Domnick, A. Lindenthal, C. Tropea, T-H. Xu, “Application of PDA in paint sprays,” Atomization Sprays 4, 273–279 (1994).
  2. U. Manasse, T. Wriedt, K. Bauchhage, “Optimization of PDA parameters for sizing of optically inhomogeneous liquid droplets,” in Proceedings of the Third Optical Particle Sizing Conference, M. Maeda, ed. (Keio University, Yokohama, 1993), pp. 453–460.
  3. U. Manasse, T. Wriedt, K. Bauchhage, “Reconstruction of real size distributions hidden in PDA results obtained from droplets of inhomogeneous liquids,” Part. Part. Syst. Charact. 11, 84–90 (1994).
    [CrossRef]
  4. C. F. Hess, G. P. Wood, “The pulse displacement technique: a single particle counter with a size range larger thant 1000:1,” in Proceedings of the Third Optical Particle Sizing Conference, M. Maeda, ed. (Keio University, Yokohama, 1993), pp. 475–482.
  5. F. Onofri, G. Gréhan, G. Gouesbet, T-H. Xu, G. Brenn, C. Tropea, “Phase Doppler anemometry with Dual Burst Technique for Particle Refractive Index Measurements,” in Proceedings of the Seventh International Symposium on Applications of Laser Techniques to Fluid Mechanics, F. Durão, ed. (Instituto Superior Técnico, Lisbon, 1994), pp. 24.1–24.9.
  6. F. Onofri, T. Girasole, G. Gréhan, G. Gouesbet, G. Brenn, J. Domnick, C. Tropea, T-H. Xu, “Phase Doppler anemometry with dual-burst technique for measurement of the refractive index and the absorption coefficient simultaneously with size and velocity,” Part. Part. Syst. Charact. 13, 112–124 (1996).
    [CrossRef]
  7. H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1957), Chaps. 4 and 12.
  8. F. Onofri, “Prise en compte de la dimension finie des faisceaux d’éclairage en granulométrie optique: anémométrie phase Doppler diagnostics des écoulements diphasiques,” Ph.D. dissertation (Université de Rouen, Rouen, France, 1995).
  9. F. Onofri, D. Blondel, G. Gréhan, G. Gouesbet, “On the optical diagnosis and sizing of coated and multilayered particles with phase Doppler anemometry,” Part. Part. Syst. Charact. 13, 104–111 (1996).
    [CrossRef]
  10. A. Naqwi, F. Durst, “Light scattering applied to LDA and PDA measurements, Part 1: theory and numerical treatments,” Part. Part. Syst. Charact. 8, 245–258 (1988).
    [CrossRef]
  11. S. V. Sankar, A. Inenaga, W. D. Bachalo, “Trajectory dependent scattering in phase Doppler interferometry: minimizing and minimizing sizing error,” in Proceedings of the Sixth Symposium on International Applications of Laser Techniques to Fluid Mechanics, F. Durão, ed. (Instituto Superior Técnico, Lisbon, 1994), pp. 12.2–12.10.
  12. G. Gréhan, G. Gouesbet, A. Naqwi, F. Durst, “Particle trajectory effects in phase Doppler systems: computations and experiments,” Part. Part. Syst. Charact. 10, 332–338 (1993).
    [CrossRef]
  13. D. Holve, S. A. Self, “Optical particle sizing for in situ measurements,” Appl. Opt. 18, 1632–1652 (1979).
    [CrossRef] [PubMed]
  14. T-H. Xu, C. Tropea, “Improving performance of a 2D phase Doppler anemometer,” Meas. Sci. Technol. 5, 969–975 (1994).
    [CrossRef]
  15. Y. Aizu, F. Durst, G. Gréhan, F. Onofri, T-H. Xu, “A PDA system without Gaussian beam defects,” in Proceedings of the Third Optical Particle Sizing Conference, M. Maeda, ed. (Keio University, Yokohama, 1993), pp. 461–470.
  16. L. Bergougnoux, J. Misguesh-Ripault, J.-L. Firpo, J. André, “Monte Carlo calculation of backscattered light intensity by suspension: comparison with experimental data,” Appl. Opt. 35, 1735–1741 (1996).
    [CrossRef] [PubMed]
  17. H. Mignon, G. Gréhan, C. Tropéa, “Measurement of cylindrical particles with phase Doppler anemometry,” Appl. Opt. 35, 5180–5187 (1996).
    [CrossRef] [PubMed]
  18. Aerometrics, Inc, 550 Del Rey Ave., Sunnyvale, Calif. 94086.
  19. Bangs Laboratories, Inc., 9025 Technology Drive, Fishers, Ind. 46038-2886.
  20. G. Gouesbet, G. Gréhan, B. Maheu, “Light scattering from a sphere arbitrarily located in a Gaussian beam, using a Bromwhich formulation,” J. Opt. Soc. Am. 5, 1427–1443 (1988).
    [CrossRef]

1996

F. Onofri, T. Girasole, G. Gréhan, G. Gouesbet, G. Brenn, J. Domnick, C. Tropea, T-H. Xu, “Phase Doppler anemometry with dual-burst technique for measurement of the refractive index and the absorption coefficient simultaneously with size and velocity,” Part. Part. Syst. Charact. 13, 112–124 (1996).
[CrossRef]

F. Onofri, D. Blondel, G. Gréhan, G. Gouesbet, “On the optical diagnosis and sizing of coated and multilayered particles with phase Doppler anemometry,” Part. Part. Syst. Charact. 13, 104–111 (1996).
[CrossRef]

L. Bergougnoux, J. Misguesh-Ripault, J.-L. Firpo, J. André, “Monte Carlo calculation of backscattered light intensity by suspension: comparison with experimental data,” Appl. Opt. 35, 1735–1741 (1996).
[CrossRef] [PubMed]

H. Mignon, G. Gréhan, C. Tropéa, “Measurement of cylindrical particles with phase Doppler anemometry,” Appl. Opt. 35, 5180–5187 (1996).
[CrossRef] [PubMed]

1994

T-H. Xu, C. Tropea, “Improving performance of a 2D phase Doppler anemometer,” Meas. Sci. Technol. 5, 969–975 (1994).
[CrossRef]

J. Domnick, A. Lindenthal, C. Tropea, T-H. Xu, “Application of PDA in paint sprays,” Atomization Sprays 4, 273–279 (1994).

U. Manasse, T. Wriedt, K. Bauchhage, “Reconstruction of real size distributions hidden in PDA results obtained from droplets of inhomogeneous liquids,” Part. Part. Syst. Charact. 11, 84–90 (1994).
[CrossRef]

1993

G. Gréhan, G. Gouesbet, A. Naqwi, F. Durst, “Particle trajectory effects in phase Doppler systems: computations and experiments,” Part. Part. Syst. Charact. 10, 332–338 (1993).
[CrossRef]

1988

A. Naqwi, F. Durst, “Light scattering applied to LDA and PDA measurements, Part 1: theory and numerical treatments,” Part. Part. Syst. Charact. 8, 245–258 (1988).
[CrossRef]

G. Gouesbet, G. Gréhan, B. Maheu, “Light scattering from a sphere arbitrarily located in a Gaussian beam, using a Bromwhich formulation,” J. Opt. Soc. Am. 5, 1427–1443 (1988).
[CrossRef]

1979

Aizu, Y.

Y. Aizu, F. Durst, G. Gréhan, F. Onofri, T-H. Xu, “A PDA system without Gaussian beam defects,” in Proceedings of the Third Optical Particle Sizing Conference, M. Maeda, ed. (Keio University, Yokohama, 1993), pp. 461–470.

André, J.

Bachalo, W. D.

S. V. Sankar, A. Inenaga, W. D. Bachalo, “Trajectory dependent scattering in phase Doppler interferometry: minimizing and minimizing sizing error,” in Proceedings of the Sixth Symposium on International Applications of Laser Techniques to Fluid Mechanics, F. Durão, ed. (Instituto Superior Técnico, Lisbon, 1994), pp. 12.2–12.10.

Bauchhage, K.

U. Manasse, T. Wriedt, K. Bauchhage, “Reconstruction of real size distributions hidden in PDA results obtained from droplets of inhomogeneous liquids,” Part. Part. Syst. Charact. 11, 84–90 (1994).
[CrossRef]

U. Manasse, T. Wriedt, K. Bauchhage, “Optimization of PDA parameters for sizing of optically inhomogeneous liquid droplets,” in Proceedings of the Third Optical Particle Sizing Conference, M. Maeda, ed. (Keio University, Yokohama, 1993), pp. 453–460.

Bergougnoux, L.

Blondel, D.

F. Onofri, D. Blondel, G. Gréhan, G. Gouesbet, “On the optical diagnosis and sizing of coated and multilayered particles with phase Doppler anemometry,” Part. Part. Syst. Charact. 13, 104–111 (1996).
[CrossRef]

Brenn, G.

F. Onofri, T. Girasole, G. Gréhan, G. Gouesbet, G. Brenn, J. Domnick, C. Tropea, T-H. Xu, “Phase Doppler anemometry with dual-burst technique for measurement of the refractive index and the absorption coefficient simultaneously with size and velocity,” Part. Part. Syst. Charact. 13, 112–124 (1996).
[CrossRef]

F. Onofri, G. Gréhan, G. Gouesbet, T-H. Xu, G. Brenn, C. Tropea, “Phase Doppler anemometry with Dual Burst Technique for Particle Refractive Index Measurements,” in Proceedings of the Seventh International Symposium on Applications of Laser Techniques to Fluid Mechanics, F. Durão, ed. (Instituto Superior Técnico, Lisbon, 1994), pp. 24.1–24.9.

Domnick, J.

F. Onofri, T. Girasole, G. Gréhan, G. Gouesbet, G. Brenn, J. Domnick, C. Tropea, T-H. Xu, “Phase Doppler anemometry with dual-burst technique for measurement of the refractive index and the absorption coefficient simultaneously with size and velocity,” Part. Part. Syst. Charact. 13, 112–124 (1996).
[CrossRef]

J. Domnick, A. Lindenthal, C. Tropea, T-H. Xu, “Application of PDA in paint sprays,” Atomization Sprays 4, 273–279 (1994).

Durst, F.

G. Gréhan, G. Gouesbet, A. Naqwi, F. Durst, “Particle trajectory effects in phase Doppler systems: computations and experiments,” Part. Part. Syst. Charact. 10, 332–338 (1993).
[CrossRef]

A. Naqwi, F. Durst, “Light scattering applied to LDA and PDA measurements, Part 1: theory and numerical treatments,” Part. Part. Syst. Charact. 8, 245–258 (1988).
[CrossRef]

Y. Aizu, F. Durst, G. Gréhan, F. Onofri, T-H. Xu, “A PDA system without Gaussian beam defects,” in Proceedings of the Third Optical Particle Sizing Conference, M. Maeda, ed. (Keio University, Yokohama, 1993), pp. 461–470.

Firpo, J.-L.

Girasole, T.

F. Onofri, T. Girasole, G. Gréhan, G. Gouesbet, G. Brenn, J. Domnick, C. Tropea, T-H. Xu, “Phase Doppler anemometry with dual-burst technique for measurement of the refractive index and the absorption coefficient simultaneously with size and velocity,” Part. Part. Syst. Charact. 13, 112–124 (1996).
[CrossRef]

Gouesbet, G.

F. Onofri, T. Girasole, G. Gréhan, G. Gouesbet, G. Brenn, J. Domnick, C. Tropea, T-H. Xu, “Phase Doppler anemometry with dual-burst technique for measurement of the refractive index and the absorption coefficient simultaneously with size and velocity,” Part. Part. Syst. Charact. 13, 112–124 (1996).
[CrossRef]

F. Onofri, D. Blondel, G. Gréhan, G. Gouesbet, “On the optical diagnosis and sizing of coated and multilayered particles with phase Doppler anemometry,” Part. Part. Syst. Charact. 13, 104–111 (1996).
[CrossRef]

G. Gréhan, G. Gouesbet, A. Naqwi, F. Durst, “Particle trajectory effects in phase Doppler systems: computations and experiments,” Part. Part. Syst. Charact. 10, 332–338 (1993).
[CrossRef]

G. Gouesbet, G. Gréhan, B. Maheu, “Light scattering from a sphere arbitrarily located in a Gaussian beam, using a Bromwhich formulation,” J. Opt. Soc. Am. 5, 1427–1443 (1988).
[CrossRef]

F. Onofri, G. Gréhan, G. Gouesbet, T-H. Xu, G. Brenn, C. Tropea, “Phase Doppler anemometry with Dual Burst Technique for Particle Refractive Index Measurements,” in Proceedings of the Seventh International Symposium on Applications of Laser Techniques to Fluid Mechanics, F. Durão, ed. (Instituto Superior Técnico, Lisbon, 1994), pp. 24.1–24.9.

Gréhan, G.

F. Onofri, D. Blondel, G. Gréhan, G. Gouesbet, “On the optical diagnosis and sizing of coated and multilayered particles with phase Doppler anemometry,” Part. Part. Syst. Charact. 13, 104–111 (1996).
[CrossRef]

H. Mignon, G. Gréhan, C. Tropéa, “Measurement of cylindrical particles with phase Doppler anemometry,” Appl. Opt. 35, 5180–5187 (1996).
[CrossRef] [PubMed]

F. Onofri, T. Girasole, G. Gréhan, G. Gouesbet, G. Brenn, J. Domnick, C. Tropea, T-H. Xu, “Phase Doppler anemometry with dual-burst technique for measurement of the refractive index and the absorption coefficient simultaneously with size and velocity,” Part. Part. Syst. Charact. 13, 112–124 (1996).
[CrossRef]

G. Gréhan, G. Gouesbet, A. Naqwi, F. Durst, “Particle trajectory effects in phase Doppler systems: computations and experiments,” Part. Part. Syst. Charact. 10, 332–338 (1993).
[CrossRef]

G. Gouesbet, G. Gréhan, B. Maheu, “Light scattering from a sphere arbitrarily located in a Gaussian beam, using a Bromwhich formulation,” J. Opt. Soc. Am. 5, 1427–1443 (1988).
[CrossRef]

F. Onofri, G. Gréhan, G. Gouesbet, T-H. Xu, G. Brenn, C. Tropea, “Phase Doppler anemometry with Dual Burst Technique for Particle Refractive Index Measurements,” in Proceedings of the Seventh International Symposium on Applications of Laser Techniques to Fluid Mechanics, F. Durão, ed. (Instituto Superior Técnico, Lisbon, 1994), pp. 24.1–24.9.

Y. Aizu, F. Durst, G. Gréhan, F. Onofri, T-H. Xu, “A PDA system without Gaussian beam defects,” in Proceedings of the Third Optical Particle Sizing Conference, M. Maeda, ed. (Keio University, Yokohama, 1993), pp. 461–470.

Hess, C. F.

C. F. Hess, G. P. Wood, “The pulse displacement technique: a single particle counter with a size range larger thant 1000:1,” in Proceedings of the Third Optical Particle Sizing Conference, M. Maeda, ed. (Keio University, Yokohama, 1993), pp. 475–482.

Holve, D.

Inenaga, A.

S. V. Sankar, A. Inenaga, W. D. Bachalo, “Trajectory dependent scattering in phase Doppler interferometry: minimizing and minimizing sizing error,” in Proceedings of the Sixth Symposium on International Applications of Laser Techniques to Fluid Mechanics, F. Durão, ed. (Instituto Superior Técnico, Lisbon, 1994), pp. 12.2–12.10.

Lindenthal, A.

J. Domnick, A. Lindenthal, C. Tropea, T-H. Xu, “Application of PDA in paint sprays,” Atomization Sprays 4, 273–279 (1994).

Maheu, B.

G. Gouesbet, G. Gréhan, B. Maheu, “Light scattering from a sphere arbitrarily located in a Gaussian beam, using a Bromwhich formulation,” J. Opt. Soc. Am. 5, 1427–1443 (1988).
[CrossRef]

Manasse, U.

U. Manasse, T. Wriedt, K. Bauchhage, “Reconstruction of real size distributions hidden in PDA results obtained from droplets of inhomogeneous liquids,” Part. Part. Syst. Charact. 11, 84–90 (1994).
[CrossRef]

U. Manasse, T. Wriedt, K. Bauchhage, “Optimization of PDA parameters for sizing of optically inhomogeneous liquid droplets,” in Proceedings of the Third Optical Particle Sizing Conference, M. Maeda, ed. (Keio University, Yokohama, 1993), pp. 453–460.

Mignon, H.

Misguesh-Ripault, J.

Naqwi, A.

G. Gréhan, G. Gouesbet, A. Naqwi, F. Durst, “Particle trajectory effects in phase Doppler systems: computations and experiments,” Part. Part. Syst. Charact. 10, 332–338 (1993).
[CrossRef]

A. Naqwi, F. Durst, “Light scattering applied to LDA and PDA measurements, Part 1: theory and numerical treatments,” Part. Part. Syst. Charact. 8, 245–258 (1988).
[CrossRef]

Onofri, F.

F. Onofri, T. Girasole, G. Gréhan, G. Gouesbet, G. Brenn, J. Domnick, C. Tropea, T-H. Xu, “Phase Doppler anemometry with dual-burst technique for measurement of the refractive index and the absorption coefficient simultaneously with size and velocity,” Part. Part. Syst. Charact. 13, 112–124 (1996).
[CrossRef]

F. Onofri, D. Blondel, G. Gréhan, G. Gouesbet, “On the optical diagnosis and sizing of coated and multilayered particles with phase Doppler anemometry,” Part. Part. Syst. Charact. 13, 104–111 (1996).
[CrossRef]

F. Onofri, G. Gréhan, G. Gouesbet, T-H. Xu, G. Brenn, C. Tropea, “Phase Doppler anemometry with Dual Burst Technique for Particle Refractive Index Measurements,” in Proceedings of the Seventh International Symposium on Applications of Laser Techniques to Fluid Mechanics, F. Durão, ed. (Instituto Superior Técnico, Lisbon, 1994), pp. 24.1–24.9.

Y. Aizu, F. Durst, G. Gréhan, F. Onofri, T-H. Xu, “A PDA system without Gaussian beam defects,” in Proceedings of the Third Optical Particle Sizing Conference, M. Maeda, ed. (Keio University, Yokohama, 1993), pp. 461–470.

F. Onofri, “Prise en compte de la dimension finie des faisceaux d’éclairage en granulométrie optique: anémométrie phase Doppler diagnostics des écoulements diphasiques,” Ph.D. dissertation (Université de Rouen, Rouen, France, 1995).

Sankar, S. V.

S. V. Sankar, A. Inenaga, W. D. Bachalo, “Trajectory dependent scattering in phase Doppler interferometry: minimizing and minimizing sizing error,” in Proceedings of the Sixth Symposium on International Applications of Laser Techniques to Fluid Mechanics, F. Durão, ed. (Instituto Superior Técnico, Lisbon, 1994), pp. 12.2–12.10.

Self, S. A.

Tropea, C.

F. Onofri, T. Girasole, G. Gréhan, G. Gouesbet, G. Brenn, J. Domnick, C. Tropea, T-H. Xu, “Phase Doppler anemometry with dual-burst technique for measurement of the refractive index and the absorption coefficient simultaneously with size and velocity,” Part. Part. Syst. Charact. 13, 112–124 (1996).
[CrossRef]

J. Domnick, A. Lindenthal, C. Tropea, T-H. Xu, “Application of PDA in paint sprays,” Atomization Sprays 4, 273–279 (1994).

T-H. Xu, C. Tropea, “Improving performance of a 2D phase Doppler anemometer,” Meas. Sci. Technol. 5, 969–975 (1994).
[CrossRef]

F. Onofri, G. Gréhan, G. Gouesbet, T-H. Xu, G. Brenn, C. Tropea, “Phase Doppler anemometry with Dual Burst Technique for Particle Refractive Index Measurements,” in Proceedings of the Seventh International Symposium on Applications of Laser Techniques to Fluid Mechanics, F. Durão, ed. (Instituto Superior Técnico, Lisbon, 1994), pp. 24.1–24.9.

Tropéa, C.

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1957), Chaps. 4 and 12.

Wood, G. P.

C. F. Hess, G. P. Wood, “The pulse displacement technique: a single particle counter with a size range larger thant 1000:1,” in Proceedings of the Third Optical Particle Sizing Conference, M. Maeda, ed. (Keio University, Yokohama, 1993), pp. 475–482.

Wriedt, T.

U. Manasse, T. Wriedt, K. Bauchhage, “Reconstruction of real size distributions hidden in PDA results obtained from droplets of inhomogeneous liquids,” Part. Part. Syst. Charact. 11, 84–90 (1994).
[CrossRef]

U. Manasse, T. Wriedt, K. Bauchhage, “Optimization of PDA parameters for sizing of optically inhomogeneous liquid droplets,” in Proceedings of the Third Optical Particle Sizing Conference, M. Maeda, ed. (Keio University, Yokohama, 1993), pp. 453–460.

Xu, T-H.

F. Onofri, T. Girasole, G. Gréhan, G. Gouesbet, G. Brenn, J. Domnick, C. Tropea, T-H. Xu, “Phase Doppler anemometry with dual-burst technique for measurement of the refractive index and the absorption coefficient simultaneously with size and velocity,” Part. Part. Syst. Charact. 13, 112–124 (1996).
[CrossRef]

J. Domnick, A. Lindenthal, C. Tropea, T-H. Xu, “Application of PDA in paint sprays,” Atomization Sprays 4, 273–279 (1994).

T-H. Xu, C. Tropea, “Improving performance of a 2D phase Doppler anemometer,” Meas. Sci. Technol. 5, 969–975 (1994).
[CrossRef]

Y. Aizu, F. Durst, G. Gréhan, F. Onofri, T-H. Xu, “A PDA system without Gaussian beam defects,” in Proceedings of the Third Optical Particle Sizing Conference, M. Maeda, ed. (Keio University, Yokohama, 1993), pp. 461–470.

F. Onofri, G. Gréhan, G. Gouesbet, T-H. Xu, G. Brenn, C. Tropea, “Phase Doppler anemometry with Dual Burst Technique for Particle Refractive Index Measurements,” in Proceedings of the Seventh International Symposium on Applications of Laser Techniques to Fluid Mechanics, F. Durão, ed. (Instituto Superior Técnico, Lisbon, 1994), pp. 24.1–24.9.

Appl. Opt.

Atomization Sprays

J. Domnick, A. Lindenthal, C. Tropea, T-H. Xu, “Application of PDA in paint sprays,” Atomization Sprays 4, 273–279 (1994).

J. Opt. Soc. Am.

G. Gouesbet, G. Gréhan, B. Maheu, “Light scattering from a sphere arbitrarily located in a Gaussian beam, using a Bromwhich formulation,” J. Opt. Soc. Am. 5, 1427–1443 (1988).
[CrossRef]

Meas. Sci. Technol.

T-H. Xu, C. Tropea, “Improving performance of a 2D phase Doppler anemometer,” Meas. Sci. Technol. 5, 969–975 (1994).
[CrossRef]

Part. Part. Syst. Charact.

G. Gréhan, G. Gouesbet, A. Naqwi, F. Durst, “Particle trajectory effects in phase Doppler systems: computations and experiments,” Part. Part. Syst. Charact. 10, 332–338 (1993).
[CrossRef]

U. Manasse, T. Wriedt, K. Bauchhage, “Reconstruction of real size distributions hidden in PDA results obtained from droplets of inhomogeneous liquids,” Part. Part. Syst. Charact. 11, 84–90 (1994).
[CrossRef]

F. Onofri, T. Girasole, G. Gréhan, G. Gouesbet, G. Brenn, J. Domnick, C. Tropea, T-H. Xu, “Phase Doppler anemometry with dual-burst technique for measurement of the refractive index and the absorption coefficient simultaneously with size and velocity,” Part. Part. Syst. Charact. 13, 112–124 (1996).
[CrossRef]

F. Onofri, D. Blondel, G. Gréhan, G. Gouesbet, “On the optical diagnosis and sizing of coated and multilayered particles with phase Doppler anemometry,” Part. Part. Syst. Charact. 13, 104–111 (1996).
[CrossRef]

A. Naqwi, F. Durst, “Light scattering applied to LDA and PDA measurements, Part 1: theory and numerical treatments,” Part. Part. Syst. Charact. 8, 245–258 (1988).
[CrossRef]

Other

S. V. Sankar, A. Inenaga, W. D. Bachalo, “Trajectory dependent scattering in phase Doppler interferometry: minimizing and minimizing sizing error,” in Proceedings of the Sixth Symposium on International Applications of Laser Techniques to Fluid Mechanics, F. Durão, ed. (Instituto Superior Técnico, Lisbon, 1994), pp. 12.2–12.10.

H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1957), Chaps. 4 and 12.

F. Onofri, “Prise en compte de la dimension finie des faisceaux d’éclairage en granulométrie optique: anémométrie phase Doppler diagnostics des écoulements diphasiques,” Ph.D. dissertation (Université de Rouen, Rouen, France, 1995).

C. F. Hess, G. P. Wood, “The pulse displacement technique: a single particle counter with a size range larger thant 1000:1,” in Proceedings of the Third Optical Particle Sizing Conference, M. Maeda, ed. (Keio University, Yokohama, 1993), pp. 475–482.

F. Onofri, G. Gréhan, G. Gouesbet, T-H. Xu, G. Brenn, C. Tropea, “Phase Doppler anemometry with Dual Burst Technique for Particle Refractive Index Measurements,” in Proceedings of the Seventh International Symposium on Applications of Laser Techniques to Fluid Mechanics, F. Durão, ed. (Instituto Superior Técnico, Lisbon, 1994), pp. 24.1–24.9.

U. Manasse, T. Wriedt, K. Bauchhage, “Optimization of PDA parameters for sizing of optically inhomogeneous liquid droplets,” in Proceedings of the Third Optical Particle Sizing Conference, M. Maeda, ed. (Keio University, Yokohama, 1993), pp. 453–460.

Y. Aizu, F. Durst, G. Gréhan, F. Onofri, T-H. Xu, “A PDA system without Gaussian beam defects,” in Proceedings of the Third Optical Particle Sizing Conference, M. Maeda, ed. (Keio University, Yokohama, 1993), pp. 461–470.

Aerometrics, Inc, 550 Del Rey Ave., Sunnyvale, Calif. 94086.

Bangs Laboratories, Inc., 9025 Technology Drive, Fishers, Ind. 46038-2886.

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Figures (12)

Fig. 1
Fig. 1

Schematic of the principle of the DBT for simultaneous measurement of the complex refractive index, size, and velocity of spherical particles in flow. D, m, and K are the particle diameter, the real part of the particle material refractive index, and the particle material absorption coefficient at the laser wavelength, respectively.

Fig. 2
Fig. 2

Attenuation of the refracted signal, by internal scattering by small scatterers, used to deduce the suspension volume concentration C v .

Fig. 3
Fig. 3

Phase Doppler modified standard geometry. Three detectors D (i) are considered with i = 1–3. The polarization of the laser beams is parallel. (The electric vector E is parallel to OY.)

Fig. 4
Fig. 4

For a modified standard geometry two symmetrical detectors can be used to eliminate trajectory effects on the signal amplitude ratio occurring for spherical particles, depending on their position along the OX axis.

Fig. 5
Fig. 5

Schematic of the experimental setup.

Fig. 6
Fig. 6

Outline of the region under study along the jet axis.

Fig. 7
Fig. 7

Typical raw Doppler signals recorded for a 120-µm liquid jet with various concentrations in suspension: The C v is = (a) 0.0049%, (b) 0.31%, (c) 0.75%, (d) 1.25%, (e) 2.5%, and (f) 5%. The suspension is a mixture of 0.35-µm spherical polystyrene particles in water (latex).

Fig. 8
Fig. 8

Monte Carlo simulations for the light intensity that is scattered in the OXZ plane by a 110-µm cylindrical particle with an axis along OY; various scatterer concentrations, d = 0.35 µm, n i = 5000, n r = 7, n p = 500.

Fig. 9
Fig. 9

Monte Carlo simulations for the evolution of the low-pass filtered amplitude of the phase Doppler signals versus the particle trajectory in the optical probe volume and for various scatterers concentrations: C v is (a) 0%, (b) 0.0125%, (c) 1.25%, (d) 2.5%, (e) 5%, (f) 10%. D = 110 µm, d = 0.35 µm, n i = 3000, n r = 7, n p = 50.

Fig. 10
Fig. 10

Comparison of the Monte Carlo and the geometric model predictions with experimental data for the evolution of the amplitude ratio with increasing scatterer concentrations. D = 120 µm, d = 0.35 µm.

Fig. 11
Fig. 11

Experimental evolution for the amplitude ratio versus the suspension concentration. Five scatterer sizes are considered. D = 120 µm, detector 3.

Fig. 12
Fig. 12

Comparison between size measurements obtained from the reflected signals (diameter deduced, D 0) and the refracted signals (diameter deduced, D 1). The expected diameter is D ≈ 220 µm.

Tables (2)

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Table 1 Optical Characteristics of Various Latex Suspensionsa

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Table 2 Optical particles of the Phase Doppler System used in the Experiment and for the Numerical Simulations

Equations (11)

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I1,Kmax=I1,0max exp-KL=I1,0max exp-NCscaL=I1,0max exp-6Cvπd3 CscaL,
I1,0maxI0max=ε12ε02tanτytanτy-tanτy.
Cv=-πd36D sinτyCscalnI1,KmaxI0max-lnε12ε02tanτytanτy-tanτy.
Ix=I0exp-2x/ωx2,
I1,Kix=I0giI1,Kmax exp-2x±x12/ωx2,
I0ix=I0giI0max exp-2x±x02/ωx2,
ψ=2τx-2 cos-1cosτx/m.
Rix=I1,KmaxI0max exp-2x±x12-x±x02/ωx2.
lnR1+lnR32=lnI1,KmaxI0max-2x12-x02ωx2.
Cv=-πd36D sinτyCscaln[R1+lnR32-lnε02ε12tanτytanτy-tanτy+2cos2τx-cos2ψ/2D2ωx2.
St=PS1+V cos2πvDt+ϕ,

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